Another aspect that explains why the vascular explanation is not enough is the resistance of the trunk in supporting the wood's weight. Also important here is the roots' structure.
When I imagine a situation where wind resistance is fundamental, I think of palm trees being subject to seasonal tropical storms, and these look nothing like the diagram in the article.
Underwater, where vascularization and weight are not as important to many branching structures like corals or algae, there is still the problem of resistance against a moving fluid. But the branching/girth/length/angle rules seem to be different.
So I'm still with team "branching optimized for sun/air exposure and constrained by vascularization, weight and root structure".
Palm trees, bamboo, corn, reeds and such are all of them quite different from the schema presented in the article. This schema seems to be some specific subset of large Eudicots, like magnolias, oaks, shrubs and such, or at any rate some paraphyletic family of plants.
In taxonomical terms, Pinophyta are even more distant from the aforementioned plants, all of them Magnoliophyta. Pine trees, cypresses and other Pinophyta branch as well, but their branching does not fit the schema in the article.
Why wasn't the hypothesis tested against the Pinophytae' specific (and quite common) kind of branching? Is surrounding fluid resistance only important for that arbitrary set of plants?
If fluid resistance, ubiquitous in plant evolution, were of such an importance in explaining a difference between what is predicted by the vascular hypothesis and what is actually observed in branching trees, the same could be said for all trees that branch, and this theory should be able to do some predictions for other branching (and non-branching) plants.
This hypothesis should have been tested for other structures right from the start, and not just for an idealized form of unwarranted generality.
But don't get me wrong: I think that it's very good to have aerospace engineers putting forth this idea, and this article adds to our understanding of tree growth and evolution. I just find it incomplete.
- calculates LOC of a top-level method
- calculates lines of code for each method called within that
- builds an hourglass visualization showing as you go up or down the abstraction layers how the LOC changes
It seems like this might be useful for seeing
- where in the abstraction layers there are major changes in density of functions
- where there is over-abstraction (many, many tiny functions)
- where there is not enough abstraction (a bulge in LOC, or overall large numbers)
Combining this with cyclomatic complexity may provide a more nuanced view for code analysis. It would allow you to quickly hone in on parts of the code-base that have too much density.
Seems so logical, for a flow in the daughter pipes to match the mother pipe... except that the wood of a tree is dead, and the flow happens in the bark... leading to a sum-rule for circumference, proportional to radii and diameter.
However, the point of a tree is structural, to get higher than other trees, higher than herbivores. Is the strength of wood proportional to cross-sectional area (required to resist gravity - the essential problem of height)? If so, that would explain the rule. Similar reasoning to wind in the article.
EDIT it also means the weight per height remains constant through branching... this doesn't seem sustainable; you'd want it to taper.
Regarding wood strength being proportional to area: it can't be as simple as that - wood is a strongly anisotropic material, so direction of loading becomes critical to understanding what's going on.
Natural trees have defects, and they "know" it. Limb attachment is messy business - in many species they are frequently defective. Doesn't reduce well to modeling actual limbs as simple beams or whatnot.
Starting to understand thigmomorphogenesis and how trees deal with it in terms of load shedding, compartmentalization, and reaction wood growth was one of my favorite "ahhh ha" moments.
This might be one of the cases when weird experimental "law" drives people away from the actual cause.
I always felt the same way about Kepler's laws. While they are true, you can't find in them any trace of actual reason why things are the way they are (conservation of energy and angular momentum in gravity field).
Angiosperms depends on tensile stresses for their strength. Trees keeping themselves upright is all about carefully distributing compressive and tensile strength in response to the environment.
Claus Mattheck's books cover this in detail.
Your so-called "causes" seem just to be more general "experimental laws". Does conservation of energy really make you feel like you understand the reason why things are the way they are?
Yes. Definitely. Definitely more than "The square of the orbital period of a planet is proportional to the cube of the semi-major axis of its orbit."
One sounds like a rule of nature, the other sounds like semi-accidental math gimmick.
I wonder how difficult it is to build wooden axis and hinges that overcome the force of friction in old carts.
This statement was unexpectedly profound.
If the area above a branching point was more than below then how would those capillaries going up to the leaves be fed?
If the area above a branching point were less than blow then how would the capillaries going down to the roots be fed?
Remember the roots fees the leaves and the leaves feed the roots. So it needs to be a balanced system.
Although researchers have previously proposed explanations for the rule based on hydraulics or structure, none of these explanations have been fully convincing. For instance, the hydraulic explanation called the “pipe model” proposes that the branching proportions have to do with the way that vascular vessels connect the tree’s roots to its leaves to provide water and nutrients. But since vascular vessels account for as little as 5% of the branch cross section (for large trunks in some tree species), it seems unlikely that they would govern the tree’s entire architecture.
It doesn't say anything new about da Vinci, and it sure doesn't seem to add anything which isn't already an accepted idea in biomechanics. The article revives vascular constraints as a strawman before beating it down again, as if it's still a theory of limb structure thats taken seriously.
My takeaway: da Vinci's rule is easily explained by modern foundational biomechanics.
* 500 years ago there hadn’t been intensive centuries-long studies of many of these phenomena, so if you wanted to know something about it the only way was to do independent investigation.
* Even for subjects which had been studied, books were rare/expensive, poorly indexed, often contained a mishmash of disorganized material, hard to track down, and often flagrantly wrong but remaining uncorrected for centuries.
* Leonardo was notoriously bad at sticking with any project, from his childhood on, easily abandoning his work and jumping to another topic, including leaving many of his paid projects unfinished. Probably serious ADHD.
* There have been many intensely curious polymaths, but in many cases they didn’t take proper notes, the notes were lost/destroyed, the notes are buried in an archive somewhere where nobody reads about them, ...
This was discussed in a great book I read called Scale:
the human vascular system follows the same rule iirc.
Firefox 62.0.3 (64-bit) on Ubuntu 14.04.